Resistances to Mass and Heat Transfer

Equation 12.121 is a modified form of the Lewis Relation, which takes into account the resistance to heat and mass transfer in the laminar sub-layer. 

The whole of die resistance to heat and mass transfer may be considered as being within the gas phase and the product of the mass transfer coefficient and the transfer surface per unit volume of column (hpa) may be taken as 0.2 s"1. 

Water is to be cooled in a small packed column from 330 to 285 K by means of air flowing countercurrently. The rate of flow of liquid is 1400 cm3/m2 s and the flow rate of the air, which enters at a temperature of 295 K and a humidity of 60%, is 3.0 m3/m2 s. Calculate the required height of tower if the whole of the resistance to heat and mass transfer may be considered as being in the gas phase and the product of the mass transfer coefficient and the transfer surface per unit volume of column is 2 s-1. 

Employing high mass velocities to minimize resistances to heat and mass transfer. 

Figure 8. Relative resistance to heat and mass transfer as a function of Biot number or hDdp/Dr...

The principles of separation have been discussed using equilibrium theory. Finite resistances to heat and mass transfer will reduce the separation achieved. 

Analytic solutions for flow around and transfer from rigid and fluid spheres are effectively limited to Re < 1 as discussed in Chapter 3. Phenomena occurring at Reynolds numbers beyond this range are discussed in the present chapter. In the absence of analytic results, sources of information include experimental observations, numerical solutions, and boundary-layer approximations. At intermediate Reynolds numbers when flow is steady and axisym-metric, numerical solutions give more information than can be obtained experimentally. Once flow becomes unsteady, complete calculation of the flow field and of the resistance to heat and mass transfer is no longer feasible. Description is then based primarily on experimental results, with additional information from boundary layer theory. 

Sublimation (or Primary Drying). For the sublimation phase of the process, the frozen material usually is subjected to a vacuum of about 4.6 millimeters of mercury. The ice-crystal sublimation process can be regarded as comprised of two basic processes (l)Heal transfer, and (2) mass transfer. In essence, heat is furnished to the ice crystals to sublime them he generated waler vapor resulting is transferred out of the sublimation interface. Thus, it is evident thal sublimation will be rare-limited by both resistances to heat and mass transfer as they occur within the material. 

This integration by quadratures works well for a number of transfer problems in burning or dissolution, for example, the burning of a sphere where the burnt ash builds up an insulating layer on the outside. With the various resistances to heat and mass transfer in series and the assumption that the... 

Particle Size and Desorption Rates. Bench-scale reactor studies of the desorption of toluene from single, 2- to 6-mm porous clay partides (14) showed desorption times that increased with the square of the particle radius, suggesting that diffusion controls the rate desorption. Parallel experiments performed in a small, pilot-scale rotary kiln at 300°C showed no effect of day partide size for diameters ranging from 0.4 to 7 mm. Additional single-partide studies with temperature profiles controlled to match those in the pilot-scale kiln had desorption times that were a factor of 2—3 shorter for the range of sizes studied (15). Hence, at the conditions examined, intrapartide mass transfer controlled the rate of desorption when single particles were involved and interpartide mass transfer controlled in a bed of particles in a rotary kiln. These results apply to full-scale kilns. As particle size is increased, intraparticle resistances to heat and mass transfer eventually begin to dominate. 

If the resistances to heat and mass transfer can be neglected, Equation S.3S or 5.36 is used for the determination of the kinetic parameters when an ideal mixing model holds, whereas Equation 5.42 or Equations 5.43 and 5.44 are used when a plug flow model is valid. For the sake of simplicity a first-order reaction is considered. The governing equations used for the determination of the chemical reaction constant are... 

The chief implication of the rising area to volume ratio is that, although the total surface area and volume is small, satellite drops may absorb significant amount of vapor due to the reduced resistance to heat and mass transfer. These findings can now be incorporated into the multi-region absorption heat and mass transfer models... 

The upper branch of the sigmoidal curve corresponds to mass transfer conditions hence, the wall temperature can be calculated by substituting Eqs. (3) and (4) in Eq. (5) and letting kr oo. Assuming that the resistances to heat and mass transfer can be represented by the film thickness and respectively, we obtain, after some algebra, Eq. (6), where the Lewis number Le represents the ratio of the heat transferring capability of the gas to the rate of diffusion mass transfer. For mixtures of methane and air, Le 1. Since... 

Important results from earlier sections are summarized here to develop reactor design strategies when external resistances to heat and mass transfer cannot be neglected. Intrapellet resistances require information about... 

ANALYSIS OF FIRST-ORDER IRREVERSIBLE CHEMICAL KINETICS IN IDEAL PACKED CATALYTIC TUBULAR REACTORS WHEN THE EXTERNAL RESISTANCES TO HEAT AND MASS TRANSFER CANNOT BE NEGLECTED... 

An experimental setup for gaseous systems is shown in Fig. 7. The actual ZLC column consists of a thin layer of adsorbent material placed between two porous sinter discs. The individual particles (or crystals) are dispersed approximately as a monolayer across the area of the sinter. This minimizes the external resistances to heat and mass transfer, so that the adsorption cell can be considered as a perfectly mixed isothermal, continuous-flow cell. The validity of this assumption has been examined in detail [52]. The isothermal approximation is generally valid for studies of diffusion in zeoHte crystals, but it can break down for strongly adsorbed species in large composite particles under conditions of macropore diffusion control. 

The one-dimensional models discussed so far neglect the resistance to heat and mass transfer in the radial direction and therefore predict uniform temperatures and conversions in a cross section. This is obviously a serious simplification when reactions with a pronounced heat effect arc involved. For such cases there is a need for a model that predicts the detailed temperature and conversion pattern in the reactor, so that the design would be directed towards avoiding eventual detrimental overtemperatures in the axis. This then leads to two-dimensional models. 

Two dimensional models permit more realistic simulation of fixed bed reactor behavior than the one-dimensional models discussed previously. Experimental measurements indicate that the fluid temperature and composition are not uniform across a section of the tube normal to the flow. The one dimensional models discussed earlier neglect the radial resistance to heat and mass transfer and thereby assume a uniform temperature and composition for each longitudinal position. This assumption is a vast oversimplification when... 

The magnitude of the resistances to heat and mass transfer through the boundary layer, i.e., the thickness of the boundary layer, depends on the velocity of the fluid relative to the catalyst particle. As this velocity increases, the heat-transfer coefficient between the bulk fluid and the surface of the catalyst particle increases and the mass-transfer coefficient between the bulk fluid and the catalyst surface increases. Therefore, the magnitude of the concentration and temperature differences between the bulk fluid and the particle surface will depend on the relative velocity, as well as on the properties of the fluid. 

The topic of transport effects in catalysis is revisited in Chapter 9. The structure of porous catalysts is discussed, and the internal and external resistances to heat and mass transfer are quantified. Special attention is devoted to helping the student understand the influence of transport effects on overall reaction behavior, including reaction selectivity. Experimental and computational methods for predicting the presence or absence of transport effects are discussed in some detail. The chapter contains examples of reactor sizing and analysis in the presence of transport effects. 

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